Let L be a regular language, accepted by a DFA M. Construct a finite automaton M_c, over the same alphabet as M, that accepts the language L_c = {x| y L such that |x| = |y|}. Let L be a regular language, accepted by a DFA M. Define the language L^1/2 = {x| y such that |x| = |y| and xy L}. In other words, L^1/2 s the language of all first halves of (even-length) strings from L. Using the ideas from your constructions in (a), construct a finite automaton that accepts L^1/2